Negative and positive numbers

In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative. Zero itself is signless, although in some contexts it makes sense to consider a signed zero, and in some contexts it makes sense to call 0 its own sign. Along with its application to real numbers, "change of sign" is used throughout mathematics and physics to denote the additive inverse (negation, or multiplication by −1), even for quantities which are not real numbers (so, which are not prescribed to be either positive, negative, or zero). Also, the word "sign" can indicate aspects of mathematical objects that resemble positivity and negativity, such as the sign of a permutation (see below).

Every number has multiple attributes (such as value, sign and magnitude). A real number is said to be positive if its value (not its magnitude) is greater than zero, and negative if it is less than zero. The attribute of being positive or negative is called the sign of the number. Zero itself is not considered to have a sign (though this is context dependent, see below). Also, signs are not defined for complex numbers, although the argument generalizes it in some sense.

In common numeral notation (which is used in arithmetic and elsewhere), the sign of a number is often denoted by placing a plus sign or a minus sign before the number. For example, +3 denotes "positive three", and −3 denotes "negative three". When no plus or minus sign is given, the default interpretation is that a number is positive. Because of this notation, as well as the definition of negative numbers through subtraction, the minus sign is perceived to have a strong association with negative numbers (of the negative sign). Likewise, "+" associates with positivity.

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